Edge strips in the quantum Hall regime imaged by a single-electron transistor

We map out compressible and incompressible strips in the depletion region of a two-dimensional electron system (2DES) in the quantum Hall regime by using a metal single-electron transistor (SET) fabricated on top of a GaAs/AlGaAs heterostructure containing the 2DES. Applying a voltage to a gate electrode at 0.9 mu m from the SET island shifts the edge of the 2DES closer to the SET island. Different edge strips are clearly resolved by monitoring the fluctuations in the current through the SET. The number of these is consistent with the value of the bulk Landau-level filling factor. [S0031-9007(98)06961-0].